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USA Math Kangaroo 2005

1. In the enchanted garden of the Green King, there are apple trees that produce golden apples.Every day, 5 golden apples become ripe on each tree, and at the end of each day they fallfrom the trees. Today, the Green Gardener has picked up 20 ripe apples that fell under thetrees last night. How many enchanted trees are there in the garden?

2. Alma, Maria, Anne and Michael had 2 apples each. Each one ate one apple. How many apples do they now have altogether?

3. Only one digit from 1 to 9 is repeated three times in this drawing.

The rest of the digits are repeated twice. Which digit is repeated three times?

4. How many different digits can you see in the picture below?

5. What number is hidden under the question mark in the picture below (on the last car):

6. 5 - 4 + 3 - 2 + 1 = ?

7. When Ann was born, Michael was 4. Now Ann is 3 years old. How old is Michael?

8. How many blocks were used to build the figure shown in the picture?

9. 4 points

Which four beads below need to be added to this string:

10. How many more square tiles do we need to put on the kitchen floor to cover all of it? (See the picture.)

11. Helga is climbing stairs in such a way that she goes up 2 steps at a time. She is standing on the third step now. On which step will she be after she moves up 3 times?

12. Some pages are missing from an open book. On the left page you can see page number 12and on the right page you can see page number 15. How many pages are missing?

13. One hen lays one egg a day. In how many days will two hens lay 6 eggs?

14. There are two horses, one duck, one fish, an eagle, and a boy in a private garden. How many legs do they have altogether?

15. Anne has some apples. Maria has 2 apples more than Anne. Altogether they have 8 apples.How many apples does Anne have?

16. Which figure is next in this sequence:

17. Monika is 2 years old and Karl is 4. How old will Monika be when Karl is 11?

18. During the race, right before the finish line, I passed the runner who won the third place.What place did I win?

19. There are three weights on the scales in the left picture: 1kg, 4 kg, 2 kg and just one weight of 1 kg on the scales in the right picture. What is the weight of the fruit in the basket?

20. Which set of signs +, - needs to be used to make this expression true?

21. The sum of two digits, one from inside the square and one from outside the square is greaterthan 10. How many such pairs can you make?

22. What number is covered by ? in the last picture below:

23. Hans fills the square table with numbers in such a way that the sum of the numbers in eachcolumn is 15 and the sum of the numbers in each row is 15 and the sum on each diagonal is15. What number will he put in place of ? in the picture below:

24. A train has four cars in four colors: red, green, white and yellow. The green car is not the firstnor the last. The yellow car is not next to the white car nor next to the red car. The first car iswhite. What is the order of the cars in that train?